How Probability Can Be Used to Design Games of Chance

One of the origins of of probability as a field in mathematics was solving games of chance. The famous correspondence between Fermat and Pascal in 1654 was one of the earliest accounts on how to use mathematics formally in order to solve a fair game of chance.

In this post, we are going to design a game that will demonstrate the power of probability. We will use probability to create a game that looks like as if it favors the player, while in reality, it favors the casino. Although most casino games actually obviously favor the casino, the game below is a bit more conservative (or should I say ‘deceptive.’)

The dice to be used in the game below is the standard 6-sided die whose number of dots are from 1 to 6. This means that the smallest possible sum is 1 + 1 = 2 and the largest possible sum is 6 + 6 = 12. Below are the instructions on how to play the game.  » Read more

The Beauty of Tessellations

Tiling is one of the many beautiful patterns that we can see around us. Some of them are man-made and some are created by nature. For example, many modern homes nowadays have tiled floors or even walls. On the other hand, in nature some animals are able to create regular tilings such as shown in the image below. Now why do bees would choose such shape?

Tiling, or popularly known as tessellation in mathematics, is not just beauty for the eyes. It has many interesting mathematical properties. For example, one question that should be asked what are the shapes that can tile a plane? What are the properties of these shapes? What are the properties of polygons that cannot tessellate the plane? Of course these questions had been answered hundreds or perhaps thousands of years ago, but they are a good exercise for the mind to those who haven’t encountered it. They are also good questions for students.  » Read more

How to Create Soap Bubbles Polyhedra

Mathematical beauty is most of the time enjoyed and appreciated by those who have knowledge mathematics. It can only be appreciated by the common person in tangible things or perhaps things that can be seen by the naked eye. Symmetry, tessellations, and patterns are several of the mathematical beauty who can be shared by math and non-math persons. Well, let’s add one more: bubbles.

The video above shows how to create soap bubbles polyhedra and other 3d shapes. Some of the polyhedra shown in the video above are tetrahedron, hexahedron, octahedron as well as some truncations. It also shows some strange behavior of bubbles when they are suspended in the air.

Enjoy watching and share the fun!

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